# Block Diagram using Integrator (Linear Systems Theory - Hespanha)

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Not sure what to do. At first I ignored what is said about using an integrator and drew the block diagram of the system, which looked a little complicated. So now, using just integrators I am stuck. If we try just taking the first system

x'1 = x1 + 4u

if we want to us an integrator, where y' = u, how can we ever draw this while satisfying the previous equation?

EDIT: Actually I think I got your hint. Is my system correct ?

## 1 Answer

You can use the following block diagram. Note that your $\boldsymbol{D}=\boldsymbol{0}$.

If you really want to have all the states you could draw it like the following picture. You can neglect all gains with $1$, if gain blocks are not allowed (for whatever crazy reason) then you can replace them by an equivalent number of signals to the summation block. eg. gain of 3 for $x_2$ will be split into three separate lines all connected to the summation block.

• i was expecting every block to be of type integrator Oct 7 '17 at 22:57
• so is my 2nd diagram not correct in my original question above? Oct 8 '17 at 20:59
• You should upload your pictures in the proper orientation. And you Block diagram is not correct, you have not gain blocks. Please have a look at my diagram. Oct 9 '17 at 12:09